ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟɉɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ
ɢɢ
ɜɪɟɦɟɧɧɵɟɜɪɟɦɟɧɧɵɟ
ɦɚɫɲɬɚɛɵɦɚɫɲɬɚɛɵ..
ȼɵɱɢɫɥɢɬɟɥɶɧɵɟȼɵɱɢɫɥɢɬɟɥɶɧɵɟ
ɦɟɬɨɞɵɦɟɬɨɞɵ
Ȼɭɩɧɶ
ɇɩɦɠɥɮɦɶ ɇɩɦɠɥɮɦɺɫɨɶɠ
ɛɨɬɛɧɜɦɣ Ʌɩɨɟɠɨɬ. ɬɣɬɭɠɧɶ
Ʌɩɧɪɩɢɣɭɶ Ʌɩɨɭɣɨɮɮɧmicroscopic (1microscopic (1--10 nm, 10 nm, fs/psfs/ps)) mesoscopicmesoscopic
(10(10--1000 nm, ns/1000 nm, ns/μμs)s) macroscopic (~1 mm, macroscopic (~1 mm, μμs/s)s/s)
QM DFT QMD MM MD MC SMD CG-MC/MD DPDLattice Models
MC-RISM RISM SCFT MD/DDFT DDFT FT-CLD
Particle-in-CellHydrodynamicsFinite ElementsFinite VolumesPeridynamics
ɘɦɠɥɭɫɩɨɨɶɠ
ɬɩɬɭɩɺɨɣɺ,ɰɣɧɣɲɠɬɥɣɠ
ɫɠɛɥɱɣɣ,ɬɭɫɮɥɭɮɫɛ
ɧɩɦɠɥɮɦ,ɬɪɠɥɭɫɶ, ɟɣɨɛɧɣɥɛ
ɋɛɝɨɩɝɠɬɨɛɺ
ɧɠɢɩɬɥɩɪɣɲɠɬɥɛɺ
ɬɭɫɮɥɭɮɫɛ,ɥɩɦɦɠɥɭɣɝɨɶɠ
ɬɝɩɤɬɭɝɛ/ɟɣɨɛɧɣɥɛ,ɪɫɩɱɠɬɬɶ
ɬɛɧɩɩɫɞɛɨɣɢɛɱɣɣ
ɧɩɦɠɥɮɦ,ɯɛɢɩɝɶɠ
ɪɠɫɠɰɩɟɶ
Ʌɫɮɪɨɩɧɛɬɳɭɛɜɨɛɺ
ɬɭɫɮɥɭɮɫɛ,ɟɠɯɩɫɧɛɱɣɺ, ɫɛɢɫɮɳɠɨɣɠ,ɭɠɲɠɨɣɠ, ɞɣɟɫɩɟɣɨɛɧɣɥɛ
ɚɬɨɦɵɚɬɨɦɵ
ɱɚɫɬɢɰɵɱɚɫɬɢɰɵ
ɱɚɫɬɢɰɵɱɚɫɬɢɰɵ//ɩɨɥɹɩɨɥɹ
ɩɨɥɹɩɨɥɹ
ɤɨɧɬɢɧɭɭɦɤɨɧɬɢɧɭɭɦee--
pp++
10-15
10-12
10-9
10-6
10-3
100
10-10 10-9 10-8 10-7 10-6 10-5 10-4
(nm) (μm)
(fs)
(ps)
(ns)
(μs)
(ms)
ɪɚɫɫɬɨɹɧɢɟ
/m
ɜɪɟɦɹ /s
Ɇɟɡɨɫɤɨɩɢɤɚ
ɩɨɥɭɷɦɩɢɪɢɱɟɫɤɢɟɦɟɬɨɞɵ
Ab initio
ɦɟɬɨɞɵ
MɋMD
Tight-Binding
MNDO, INDO/S
Ʉɨɧɬɢɧɭɚɥɶɧɵɟ
ɦɟɬɨɞɵ
Lattice Monte Carlo
Brownian Dynamics
Dissipative Particle Dynamics
Field Theoretic Methods
Ⱥɬɨɦɢɫɬɢɱɟɫɤɢɟ
ɦɟɬɨɞɵ
~102 ~103
~106
~109
~NAv
Ƚɥɚɜɧɵɣ
ɜɵɡɨɜ: ɦɭɥɶɬɢɦɚɫɲɬɚɛɧɨɟ
ɦɨɞɟɥɢɪɨɜɚɧɢɟ
ɍɍɫɪɟɞɧɟɧɢɟɫɪɟɞɧɟɧɢɟ
ɩɨɩɨ
ɜɪɟɦɟɧɢɜɪɟɦɟɧɢɋɪɟɞɧɟɟ
ɡɧɚɱɟɧɢɟ
<Ⱥ> ɧɟɤɨɬɨɪɨɝɨ
ɫɜɨɣɫɬɜɚ
Ⱥ(r,v), ɡɚɜɢɫɹɳɟɝɨ
ɨɬ
ɤɨɨɪɞɢɧɚɬ
{r} ɢ
ɫɤɨɪɨɫɬɟɣ
{v} ɱɚɫɬɢɰ, ɨɩɪɟɞɟɥɹɸɬ
ɩɭɬɟɦ
ɭɫɪɟɞɧɟɧɢɹ
ɦɧɨɠɟɫɬɜɚ
"ɦɝɧɨɜɟɧɧɵɯ" ɡɧɚɱɟɧɢɣ
A[r(t),v(t)], ɧɚɛɥɸɞɚɟɦɵɯ
ɜ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ
ɦɨɦɟɧɬɵ
ɜɪɟɦɟɧɢ
t. Ɍɚɤɨɣ
ɩɨɞɯɨɞ
ɢɫɯɨɞɢɬ
ɢɡ
ɬɨɝɨ, ɱɬɨ
ɧɚɦ
ɢɡɜɟɫɬɧɵ
ɡɚɤɨɧɵ
ɞɜɢɠɟɧɢɹ
ɱɚɫɬɢɰ
ɫɢɫɬɟɦɵ.
ɍɍɫɪɟɞɧɟɧɢɟɫɪɟɞɧɟɧɢɟ
ɩɨɩɨ
ɚɧɫɚɦɛɥɸɚɧɫɚɦɛɥɸɇɚɛɥɸɞɚɟɦɨɟ
ɫɜɨɣɫɬɜɨ
ɪɚɫɫɦɚɬɪɢɜɚɸɬ
ɤɚɤ
ɫɪɟɞɧɟɟ
ɩɨɦɧɨɠɟɫɬɜɭ
ɪɚɡɥɢɱɧɵɯ
ɫɨɫɬɨɹɧɢɣɫɢɫɬɟɦɵ, ɤɨɬɨɪɵɟ
ɜɨɡɧɢɤɚɸɬ
ɫɨɩɪɟɞɟɥɟɧɧɨɣ
ɜɟɪɨɹɬɧɨɫɬɶɸ. ȼɟɪɨɹɬɧɨɫɬɶ
(ɱɚɫɬɨɬɚ) ɜɨɡɧɢɤɧɨɜɟɧɢɹ
ɬɨɝɨ
ɢɥɢ
ɢɧɨɝɨɫɨɫɬɨɹɧɢɹ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ
ɟɝɨɫɬɚɬɢɫɬɢɱɟɫɤɨɦɭ
ɜɟɫɭ
e–U/kT,ɝɞɟ
U
–
ɩɨɬɟɧɰɢɚɥɶɧɚɹ
ɷɧɟɪɝɢɹ
ɞɚɧɧɨɣɤɨɧɮɢɝɭɪɚɰɢɢ, k
–
ɤɨɧɫɬɚɧɬɚ
Ȼɨɥɶɰɦɚɧɚ, T –ɚɛɫɨɥɸɬɧɚɹ
ɬɟɦɩɟɪɚɬɭɪɚ.
ȾɜɚȾɜɚ
ɩɨɞɯɨɞɚɩɨɞɯɨɞɚ
ɜɜ
ɫɬɚɬɢɫɬɢɱɟɫɤɨɣɫɬɚɬɢɫɬɢɱɟɫɤɨɣ
ɬɟɨɪɢɢɬɟɨɪɢɢ
ɈɛɚɈɛɚ
ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ
ɩɪɢɧɰɢɩɚɩɪɢɧɰɢɩɚ
ɦɨɝɭɬɦɨɝɭɬ
ɛɵɬɶɛɵɬɶ
ɩɨɥɨɠɟɧɵɩɨɥɨɠɟɧɵ
ɜɜ
ɨɫɧɨɜɭɨɫɧɨɜɭ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯɜɵɱɢɫɥɢɬɟɥɶɧɵɯ
ɫɯɟɦɫɯɟɦ, , ɪɟɚɥɢɡɭɟɦɵɯɪɟɚɥɢɡɭɟɦɵɯ
ɧɚɧɚ
ɤɨɦɩɶɸɬɟɪɟɤɨɦɩɶɸɬɟɪɟ. . ɇɇɟɨɛɯɨɞɢɦɨɟɨɛɯɨɞɢɦɨ
ɡɧɚɬɶɡɧɚɬɶ
ɥɢɲɶɥɢɲɶɫɩɨɫɨɛɫɩɨɫɨɛ
ɪɚɫɱɟɬɚɪɚɫɱɟɬɚ
ɩɨɬɟɧɰɢɚɥɶɧɨɣɩɨɬɟɧɰɢɚɥɶɧɨɣ
ɷɧɟɪɝɢɢɷɧɟɪɝɢɢ
ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ
UU
ɤɚɤɤɚɤ
ɮɭɧɤɰɢɢɮɭɧɤɰɢɢ
ɤɨɨɪɞɢɧɚɬɤɨɨɪɞɢɧɚɬ rr..
ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ
ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ
mmii
aaii
((tt) = ) = FFii
((tt) ) [[ɦɚɫɫɚɦɚɫɫɚ
××
ɭɫɤɨɪɟɧɢɟɭɫɤɨɪɟɧɢɟ
= = ɫɢɥɚɫɢɥɚ]]
aaii
((tt) = d) = dvvii
((tt)/)/ddtt
= d= d22rrii
((tt)/d)/dtt22
FFii
((tt) = ) = ––∂∂UU((rr11
,,……, , rrNN
))//∂∂rrii
ɇɭɠɧɨ
ɡɧɚɬɶ
ɥɢɲɶ
U(r1,…, rN)
ɢɥɢ
F
!
mm
ii
dd22rrii
((tt)/d)/dtt22
= = FFii
((tt))
John von
NeumannGrand Monaco ɋasino
ɆɨɧɬɟɆɨɧɬɟ--ɄɚɪɥɨɄɚɪɥɨ
SA
=nA
/n
ǞǸȀȄǭǶǺǭȌ
ǯȈǮǻǽǷǭ
∑ωω=−ωj
jjjjj pkTU /)/exp(~
∑∑
−
−
=
j
kTU
j
kTU
j
j
j
e
eA
A /
/
ǞǿǭǿǵǾǿǵȄDzǾǷǵǶ
ǯDzǾ
ǷǻǺȁǵǰȀǽǭȃǵǵ
1944 ǰǻDZ
ɆɨɧɬɟɆɨɧɬɟ--ɄɚɪɥɨɄɚɪɥɨ
((ɦɟɬɨɞɦɟɬɨɞ
ɆɟɬɪɨɩɨɥɢɫɚɆɟɬɪɨɩɨɥɢɫɚ
––
""ɫɭɳɟɫɬɜɟɧɧɚɹɫɭɳɟɫɬɜɟɧɧɚɹ
ɜɵɛɨɪɤɚɜɵɛɨɪɤɚ")")
(1953) Metropolis, (1953) Metropolis, RosenbluthRosenbluth, , RosenbluthRosenbluth, Teller, Teller, Teller, Teller
= = MRMR22TT22
∑=
=s
n
nAs
A1
1
{r}→U {r'}→U' Ⱦɥɹ
{r} ɧɚɣɬɢ
U
ɢ
ω=exp(-U/kT)
ɋɥɭɱɚɣɧɨ
ɜɵɛɪɚɬɶ
ɱɚɫɬɢɰɭ
i
ɋɥɭɱɚɣɧɨ
ɩɟɪɟɦɟɫɬɢɬɶ
ɱɚɫɬɢɰɭ
i:r'i
→ri
+Δr; {r}→{r'}
ɇɚɣɬɢ
U' ɢ ɜɟɫ ω'=exp(-U'/kT)
Ɂɚɦɟɧɢɬɶ
{r}
ɧɚ
{r'}
ɫ
ɜɟɪɨɹɬɧɨɫɬɶɸ
p
= min{1, ω'/ ω}
ɉɟɪɢɨɞɢɱɟɫɤɢɟɉɟɪɢɨɞɢɱɟɫɤɢɟ
ɝɪɚɧɢɱɧɵɟɝɪɚɧɢɱɧɵɟ
ɭɫɥɨɜɢɹɭɫɥɨɜɢɹ
3D
ǿǻǽ
/ 2D ǾǵǾǿDzǹǭ ←←
LL →→
4D
ǷȀǮ
-
ǿDzǾǾDzǽǭǷǿ
ǻǮǽǭǴ
Ɉɩɪɟɞɟɥɟɧɢɟ
1. ɉɨɧɹɬɢɟɉɨɧɹɬɢɟ
""ɦɨɞɟɥɶɦɨɞɟɥɶ
ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ" " ɡɚɤɥɸɱɚɟɬɫɹɡɚɤɥɸɱɚɟɬɫɹ
ɜɜ
ɜɵɛɨɪɟɜɵɛɨɪɟ
ɩɪɚɜɢɥɩɪɚɜɢɥ, , ɨɩɢɫɵɜɚɸɳɢɯɨɩɢɫɵɜɚɸɳɢɯ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɜɡɚɢɦɨɞɟɣɫɬɜɢɟ
ɱɚɫɬɢɰɱɚɫɬɢɰ
ɦɟɠɞɭɦɟɠɞɭ
ɫɨɛɨɣɫɨɛɨɣ
ɢɢ//ɢɥɢɢɥɢ
ɫɫ
ɜɧɟɲɧɢɦɢɜɧɟɲɧɢɦɢ
ɩɨɥɹɦɢɩɨɥɹɦɢ, , ɬɬ..ɟɟ. . ɜɜ
ɮɨɪɦɭɥɢɪɨɜɤɟɮɨɪɦɭɥɢɪɨɜɤɟ
ɜɢɞɚɜɢɞɚ
ɢɢ
ɫɩɨɫɨɛɚɫɩɨɫɨɛɚ
ɜɵɱɢɫɥɟɧɢɹɜɵɱɢɫɥɟɧɢɹ
ɮɭɧɤɰɢɢɮɭɧɤɰɢɢ
ɩɨɬɟɧɰɢɚɥɶɧɨɣɩɨɬɟɧɰɢɚɥɶɧɨɣ
ɷɧɟɪɝɢɢɷɧɟɪɝɢɢ..
ǚȀdzǺǻ
ǴǺǭǿȉ:
U(r1
,…, rN
)
ɏɨɪɨɲɚɹ
ɬɟɨɪɢɹ
ɫɥɨɠɧɵɯ
ɫɢɫɬɟɦ
ɞɨɥɠɧɚ ɩɪɟɞɫɬɚɜɥɹɬɶ
ɫɨɛɨɣ
ɥɢɲɶ
ɯɨɪɨɲɭɸ "ɤɚɪɢɤɚɬɭɪɭ" ɧɚ
ɷɬɢ
ɫɢɫɬɟɦɵ, ɭɬɪɢɪɭɸɳɭɸɬɟ
ɫɜɨɣɫɬɜɚ
ɢɯ, ɤɨɬɨɪɵɟ
ɹɜɥɹɸɬɫɹ
ɧɚɢɛɨɥɟɟɬɢɩɢɱɟɫɤɢɦɢ, ɢ
ɭɦɵɲɥɟɧɧɨ
ɢɝɧɨɪɢɪɭɸɳɭɸɜɫɟ
ɨɫɬɚɥɶɧɵɟ
-
ɧɟɫɭɳɟɫɬɜɟɧɧɵɟ
ɫɜɨɣɫɬɜɚ.
ə.ɂ. Ɏɪɟɧɤɟɥɶ
Ɉɩɪɟɞɟɥɟɧɢɟ
2. Ʉɨɦɩɶɸɬɟɪɧɚɹ
ɢɦɢɬɚɰɢɹ
ɦɟɬɨɞɚɦɢ
ɦɨɥɟɤɭɥɹɪɧɨɣ
ɞɢɧɚɦɢɤɢ
ɢɥɢ
Ɇɨɧɬɟ-Ʉɚɪɥɨ
ɦɨɞɟɥɢ
ɮɢɡɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɵ
ɫ
ɰɟɥɶɸ
ɢɡɭɱɟɧɢɹ
ɟɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɜ
ɡɚɜɢɫɢɦɨɫɬɢ
ɨɬ
ɡɚɞɚɧɧɵɯ
ɩɚɪɚɦɟɬɪɨɜ
ɩɪɟɞɫɬɚɜɥɹɟɬ
ɫɨɛɨɣ
ɱɢɫɥɟɧɧɵɣ
(ɤɨɦɩɶɸɬɟɪɧɵɣ) ɷɤɫɩɟɪɢɦɟɧɬ
ɫ ɷɬɨɣ
ɦɨɞɟɥɶɸ.
ɍɬɜɟɪɠɞɟɧɢɟ
1. ɉɨɫɤɨɥɶɤɭ
ɦɟɬɨɞɵ
ɆȾ
ɢ
ɆɄ
ɨɫɧɨɜɵɜɚɸɬɫɹ
ɧɚ
ɜɟɫɶɦɚ
ɨɛɳɢɯ
ɩɪɢɧɰɢɩɚɯ
ɤɥɚɫɫɢɱɟɫɤɨɣ
ɮɢɡɢɤɢ, ɨɧɢ ɜ ɫɭɳɧɨɫɬɢ
ɩɪɟɞɫɬɚɜɥɹɸɬ
ɫɨɛɨɣ
ɥɢɲɶ
ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ
(ɱɢɫɥɟɧɧɭɸ) ɪɟɚɥɢɡɚɰɢɸ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ
ɩɨɞɯɨɞɨɜ
ɤ
ɨɩɪɟɞɟɥɟɧɢɸ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɫɢɫɬɟɦɵ
ɢɫɯɨɞɹ
ɢɡ
ɡɚɞɚɧɧɵɯ
ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɯ
ɡɚɤɨɧɨɜ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɱɚɫɬɢɰ.
ɉɨɷɬɨɦɭ, ɟɫɥɢ
ɜ
ɦɨɞɟɥɢɪɭɸɳɟɣ
ɩɪɨɝɪɚɦɦɟ
ɧɟɬ
ɨɲɢɛɨɤ
ɢ
ɩɪɟɞɭɫɦɨɬɪɟɧ
ɧɚɞɥɟɠɚɳɢɣ
ɤɨɧɬɪɨɥɶ
ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ
ɩɨɝɪɟɲɧɨɫɬɟɣ, ɬɨ
ɩɨɥɭɱɟɧɧɵɟ
ɪɟɡɭɥɶɬɚɬɵ
ɛɭɞɭɬ
ɫɬɪɨɝɢɦɢ, ɬɨ
ɟɫɬɶ
ɢɦɟɸɳɢɦɢ
ɫɢɥɭ
ɚɤɫɢɨɦɵ
ɞɥɹ
ɜɵɛɪɚɧɧɨɣ
ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ
ɦɨɞɟɥɢ
ɮɢɡɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɵ.
ȺɞɢɚɛɚɬɢɱɟɫɤɨɟȺɞɢɚɛɚɬɢɱɟɫɤɨɟ
ɩɪɢɛɥɢɠɟɧɢɟɩɪɢɛɥɢɠɟɧɢɟ((ɦɟɬɨɞɦɟɬɨɞ
ɦɨɥɟɤɭɥɹɪɧɨɣɦɨɥɟɤɭɥɹɪɧɨɣ
ɦɟɯɚɧɢɤɢɦɟɯɚɧɢɤɢ))
ɉɪɢɛɥɢɠɟɧɢɟɉɪɢɛɥɢɠɟɧɢɟ
ȻɨɪɧɚȻɨɪɧɚ--ɈɩɩɟɧɝɟɣɦɟɪɚɈɩɩɟɧɝɟɣɦɟɪɚ
ɞɥɹɞɥɹ
ɭɪɭɪ. . ɒɪɺɞɢɧɝɟɪɚɒɪɺɞɢɧɝɟɪɚ..ǬȍȒȖȔȗȖȏȐȞȐȧǬȍȒȖȔȗȖȏȐȞȐȧ
ȊȖȓȕȖȊȖȑȊȖȓȕȖȊȖȑ
ȜțȕȒȞȐȐȜțȕȒȞȐȐ
ȕȈȕȈ
ȥȓȍȒȚȘȖȕȕțȦȥȓȍȒȚȘȖȕȕțȦ
ȐȐ
ȧȌȍȘȕțȦȧȌȍȘȕțȦ
ȟȈșȚȐȟȈșȚȐ::……ȌȊȐȎȍȕȐȍȌȊȐȎȍȕȐȍ
ȒȈȎȌȖȋȖȒȈȎȌȖȋȖ
ȥȓȍȒȚȘȖȕȈȥȓȍȒȚȘȖȕȈ
ȊȊ
ȈȚȖȔȍȈȚȖȔȍ
ȐȓȐȐȓȐ
ȔȖȓȍȒțȓȍȔȖȓȍȒțȓȍ
ȔȖȎȍȚȔȖȎȍȚ
ȘȈșșȔȈȚȘȐȊȈȚȤșȧȘȈșșȔȈȚȘȐȊȈȚȤșȧȕȍȏȈȊȐșȐȔȖȕȍȏȈȊȐșȐȔȖ
ȖȚȖȚ
ȌȊȐȎȍȕȐȧȌȊȐȎȍȕȐȧ
ȈȚȖȔȕȖȋȖȈȚȖȔȕȖȋȖ
ȧȌȘȈȧȌȘȈ
ȐȓȐȐȓȐ
șȐșȚȍȔȣșȐșȚȍȔȣ
ȈȚȖȔȕȣȝȈȚȖȔȕȣȝ
ȧȌȍȘȧȌȍȘ......
"ɉɨɥɭɤɥɚɫɫɢɱɟɫɤɢɟ" ɩɪɢɛɥɢɠɟɧɢɟ.ɋɬɚɬɢɫɬɢɱɟɫɤɚɹ
ɫɭɦɦɚ:
Q = Qclass
Qquant
((M/mM/mee
=1830)=1830)
ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ
ɦɨɞɟɥɶɦɨɞɟɥɶ
ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ((ɦɨɥɟɤɭɥɹɪɧɚɹɦɨɥɟɤɭɥɹɪɧɚɹ
ɦɟɯɚɧɢɤɚɦɟɯɚɧɢɤɚ))
ɷɥɟɤɬɪɨɧɧɨɷɥɟɤɬɪɨɧɧɨ--ɹɞɟɪɧɚɹɹɞɟɪɧɚɹ
ɫɢɫɬɟɦɚɫɢɫɬɟɦɚ""ȺɬɨɦȺɬɨɦ""
""ɆɨɥɟɤɭɥɚɆɨɥɟɤɭɥɚ""
∑ ∑+= nvvalmol UUU
∑=molecules
molUU
ǜǻǿDzǺȃǵǭǸȉǺǭȌ
ȊǺDzǽǰǵȌ
ǹǻǸDzǷȀǸȈ
ǵ
ǹǻǸDzǷȀǸȌǽǺǻǶ
ǾǵǾǿDzǹȈ
ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ
ɦɨɞɟɥɶɦɨɞɟɥɶ
ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ:: ȼɧɭɬɪɟɧɧɢɟȼɧɭɬɪɟɧɧɢɟ
ɤɨɨɪɞɢɧɚɬɵɤɨɨɪɞɢɧɚɬɵ
)]cos(1[
)(
)(
02
1
202
1
202
1
ϕ±=
Θ−Θ=
−=
Θ
nVU
kU
bbkU
tors
angle
bbond
ȼɧɭɬɪɢɦɨɥɟɤɭɥɹɪɧɵɟ"ɜɚɥɟɧɬɧɵɟ" ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
...
∑∑∑
+
+
+=
tors
tors
angle
angle
bond
bondval
U
U
UU
ɆɟɯɚɧɢɱɟɫɤɚɹɆɟɯɚɧɢɱɟɫɤɚɹ
ɦɨɞɟɥɶɦɨɞɟɥɶ
ɦɨɥɟɤɭɥɵɦɨɥɟɤɭɥɵ:: ɇɟɜɚɥɟɧɬɧɵɟɇɟɜɚɥɟɧɬɧɵɟ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
⎟⎟⎠
⎞⎜⎜⎝
⎛ σ−
σε=
6
6
12
12
4)(rr
rUVdW
YH...OX10
10
12
12
cos4)( −−− Θ⎟⎟⎠
⎞⎜⎜⎝
⎛ σ−
σε=
rrrU HbondH
r
qqU el
o
21
∈=
ɉɨɬɟɧɰɢɚɥɉɨɬɟɧɰɢɚɥ
ɅɟɧɧɚɪɞɚɅɟɧɧɚɪɞɚ--ȾɠɨɧɫɚȾɠɨɧɫɚ
ȼɨɞɨɪɨɞɧɚɹȼɨɞɨɪɨɞɧɚɹ
ɫɜɹɡɶɫɜɹɡɶ
ɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ
((ɩɨɬɟɧɰɢɚɥɩɨɬɟɧɰɢɚɥ
ɄɭɥɨɧɚɄɭɥɨɧɚ))
2/1
,1
2
,1
)1(2exp
)1(exp
⎭⎬⎫
⎩⎨⎧
⎥⎦
⎤⎢⎣
⎡−−−
−⎥⎦
⎤⎢⎣
⎡−−⋅=
∑
∑
≠=
≠=
jij Me
ij
jij Me
ij
i
D
rQB
D
rCAu
ȼɡɚɢɦɨɞɟɣɫɬɜɢɟȼɡɚɢɦɨɞɟɣɫɬɜɢɟ
ɦɟɬɚɥɥɦɟɬɚɥɥ--ɦɟɬɚɥɥɦɟɬɚɥɥ
( ) K1010
88
66
r
C
r
C
r
Crudis −−−=
( ) ( ) Br
overlap erAru −≈
ǟǽǵǟǽǵ
ǼȀǿǵǼȀǿǵ
ǷǷ
NanoNano…… ǵǵ
DZǭǸDzDzDZǭǸDzDz
•• ǗǽȀǼǺǻǹǭǾȅǿǭǮǺǻDzǗǽȀǼǺǻǹǭǾȅǿǭǮǺǻDz
ǭǿǻǹǵǾǿǵȄDzǾǷǻDzǭǿǻǹǵǾǿǵȄDzǾǷǻDz ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz
––
ǽǭǾǼǭǽǭǸǸDzǸDzǺǺȈDzǽǭǾǼǭǽǭǸǸDzǸDzǺǺȈDz
ǵǵ ǽǭǾǼǽDzDZDzǸDzǺǺȈDzǽǭǾǼǽDzDZDzǸDzǺǺȈDz
ǯȈȄǵǾǸDzǺǵȌǯȈȄǵǾǸDzǺǵȌ ((ǾȀǼDzǽǷǻǹǼȉȋǿDzǽȈǾȀǼDzǽǷǻǹǼȉȋǿDzǽȈ
ǵǵ
GRIDGRID--ǾǵǾǿDzǹȈǾǵǾǿDzǹȈ))..
•• ǕǾǼǻǸȉǴǻǯǭǺǵDzǕǾǼǻǸȉǴǻǯǭǺǵDz
ǻǰǽȀǮǸDzǺǺȈȂǻǰǽȀǮǸDzǺǺȈȂ
ǹǻDZDzǸDzǶǹǻDZDzǸDzǶ: : ǹDzǴǻǾǷǻǼǵȄDzǾǷǵDzǹDzǴǻǾǷǻǼǵȄDzǾǷǵDz
ǹDzǿǻDZȈǹDzǿǻDZȈ..
•• ǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDzǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDz
ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz:: ȄǭǾǿǵȃȈȄǭǾǿǵȃȈ
+ + ǼǻǸȌǼǻǸȌ..
ȼɵɫɨɤɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɵɟȼɵɫɨɤɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɵɟ
ɜɵɱɢɫɥɢɬɟɥɶɧɵɟɜɵɱɢɫɥɢɬɟɥɶɧɵɟ
ɫɢɫɬɟɦɵɫɢɫɬɟɦɵ
Cluster SKIF-MSU5080 CPUs4-core Intel Xeon E5472 3.0 GHz~70 TFLOPS
Blue Gene/P8192 CPUs
GRID-ǾǵǾǿDzǹȈ
((1 1 TFLOPS = TFLOPS = 1 1 ȚȘȓȕȚȘȓȕ
ȖȗȍȘȈȞȐȑȖȗȍȘȈȞȐȑ
ȊȊ
șȍȒțȕȌțșȍȒțȕȌț))
ȼɢɪɭɫɵȼɢɪɭɫɵ
VirusX: 713,580 ɚɬɨɦɨɜ
Satellite Tobacco Mosaic Virus:
932,508 ɚɬɨɦɨɜPenicillium
stoloniferum
F
(PsV-F):
5,000,000 ɚɬ. (120 ɤɨɩɢɣ ɨɞɧɨɝɨ ɛɟɥɤɚ)
ȼɢɪɭɫɵȼɢɪɭɫɵ: : ɆɨɥɟɤɭɥɹɪɧɚɹɆɨɥɟɤɭɥɹɪɧɚɹ
ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ
Satellite Tobacco Mosaic Virus:
932,508 ɚɬɨɦɨɜ
20 Ǻǹ~10 ǺǾ
ɉɨɥɢɦɟɪɧɵɟɉɨɥɢɦɟɪɧɵɟ
ɷɥɟɤɬɪɨɥɢɬɧɵɟɷɥɟɤɬɪɨɥɢɬɧɵɟ
ɬɨɩɥɢɜɧɵɟɬɨɩɥɢɜɧɵɟ
ɷɥɟɦɟɧɬɵɷɥɟɦɟɧɬɵ
Ƀɩɨɩɧɠɫɨɛɺ
ɧɠɧɜɫɛɨɛ
–
ɸɭɩ
ɩɜɶɲɨɩ
Nafion®
:
water/methanol + mobile ions
Ⱦɣɟɫɩɯɣɦɷɨɶɠ
ɥɛɨɛɦɶ
–ɣɧɠɨɨɩ
ɩɨɣ
ɪɫɩɝɩɟɺɭ
ɭɩɥ.
ɇɚɧɨɤɨɦɩɨɡɢɬɵɇɚɧɨɤɨɦɩɨɡɢɬɵȺɥɸɦɨɫɢɥɢɤɚɬ
Na+, K+ ɉɨɥɢɦɟɪ/ɜɨɞɚ
xxxxxxx
y x
z
US US TeraGrid/GridSAMTeraGrid/GridSAM
~107
ɚɬɨɦɨɜ
ɇɚɧɨɩɪɨɜɨɞɚɇɚɧɨɩɪɨɜɨɞɚ
ɧɚɧɚ
ɨɫɧɨɜɟɨɫɧɨɜɟ
ȾɇɄȾɇɄ
Ɇɟɬɚɥɥɢɱɟɫɤɢɟ
ɩɪɨɜɨɞɚ:
Ȼɨɥɶɲɨɟ
ɩɨɜɟɪɯɧɨɫɬɧɨɟ
ɧɚɬɹɠɟɧɢɟɜɟɞɟɬ
ɤ
ɞɟɮɨɪɦɚɰɢɢ
ɢ
ɪɚɡɪɵɜɭ
Ɇɟɬɚɥɥɢɡɚɰɢɹ
ȾɇɄ:1. Ʉɨɧɞɟɧɫɚɰɢɹ
Au+3
2. ȼɨɫɫɬɚɧɨɜɥɟɧɢɟ
Au+3
→ Au
Ȼɦɷɭɠɫɨɛɭɣɝɛ
MD with many-body potential
ɋɚɦɨɫɛɨɪɤɚ
ɧɚɧɨɱɚɫɬɢɰ
ɡɨɥɨɬɚɧɚ
ɩɨɜɟɪɯɧɨɫɬɢ
ȾɇɄ.
ɉɪɨɛɥɟɦɚɉɪɨɛɥɟɦɚ ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢ ɦɨɥɟɤɭɥɦɨɥɟɤɭɥ
ɋɬɪɚɬɟɝɢɹ:1.
ɉɪɟɞɫɤɚɡɚɬɶ
ɤɪɢɫɬɚɥɥ.2.
Ɋɚɡɦɧɨɠɢɬɶ
ɤɪɢɫɬɚɥɥ.3.
ɆȾ
ɦɨɞɟɥɢɪɨɜɚɧɢɟ.
ɬɢɨɮɟɧ
ɩɟɩɬɢɞ
ɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ ɦɨɞɟɥɢɦɨɞɟɥɢ (Coarse(Coarse--graining)graining)
•• ǜǻǺǵdzDzǺǵDzǜǻǺǵdzDzǺǵDz
ȄǵǾǸǭȄǵǾǸǭ
ǾǿDzǼDzǺDzǶǾǿDzǼDzǺDzǶ
ǾǯǻǮǻDZȈǾǯǻǮǻDZȈ [United Atoms (UA), Mapping/Reverse [United Atoms (UA), Mapping/Reverse
MappingMapping, , SMD, DPD].SMD, DPD].
•• ǛǮǻǸǻȄǷǵǛǮǻǸǻȄǷǵ
[Shape[Shape--based Models, Patchy based Models, Patchy Particles, Granular Models]Particles, Granular Models]..
•• ǑǵǾǷǽDzǿǺȈDzǑǵǾǷǽDzǿǺȈDz
ǽDzȅDzǿǻȄǺȈDzǽDzȅDzǿǻȄǺȈDz
ǹǻDZDzǸǵǹǻDZDzǸǵ. .
ɋɬɨɯɚɫɬɢɱɟɫɤɚɹɋɬɨɯɚɫɬɢɱɟɫɤɚɹ
ɦɨɥɟɤɭɥɹɪɧɚɹɦɨɥɟɤɭɥɹɪɧɚɹ
ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ
Robert Brown (1773-1858)
6 /frictiona F vγ πη= = −Ɂɚɤɨɧ
ɋɬɨɤɫɚ
ɞɥɹ
ɤɨɷɮɮɢɰɢɟɧɬɚ
ɬɪɟɧɢɹ
6
kTD
aπη=
)(tvvm σςγ +−=&ɍɪɚɜɧɟɧɢɟ
Ʌɚɧɠɟɜɟɧɚ
0)( =tς )()()( tttt ′−=′ δςς
σTkB2/2σ=γ
RandomFrictionveConservatidt
dm FFF
r++=
2
2
RandomveConservatidt
dm FF
r+=
Ʌɚɧɠɟɜɟɧɨɜɚ
ɞɢɧɚɦɢɤɚ
Ȼɪɨɭɧɨɜɫɤɚɹ
ɞɢɧɚɦɢɤɚ
ɈɝɪɭɛɥɟɧɢɟɈɝɪɭɛɥɟɧɢɟ
ɦɨɞɟɥɢɦɨɞɟɥɢ
((CoarseCoarse--Graining, CG)Graining, CG)ɉɨɧɢɠɟɧɢɟɉɨɧɢɠɟɧɢɟ
ɱɢɫɥɚɱɢɫɥɚ
ɫɬɟɩɟɧɟɣɫɬɟɩɟɧɟɣ
ɫɜɨɛɨɞɵɫɜɨɛɨɞɵ
MappingMapping
ɆɨɞɟɥɶɆɨɞɟɥɶ
ɩɨɥɢɦɟɪɢɡɚɰɢɢɩɨɥɢɦɟɪɢɡɚɰɢɢ
((ɯɢɦɢɱɟɫɤɚɹɯɢɦɢɱɟɫɤɚɹ
ɫɟɬɤɚɫɟɬɤɚ))
ɋɯɟɦɚɋɯɟɦɚ
ɫɜɹɡɟɣɫɜɹɡɟɣ
ɌɨɩɨɥɨɝɢɹɌɨɩɨɥɨɝɢɹ
ɫɟɬɤɢɫɟɬɤɢ
Reverse MappingReverse Mapping
ɆɄɆɄ
ɆȾɆȾ
23867
points
500
points
100
points
ɒɚɪɧɢɪɵɒɚɪɧɢɪɵ
ɢɢ
ɨɛɨɥɨɱɤɢɨɛɨɥɨɱɤɢ
Shape-based coarse-graining Ⱦɟɮɨɪɦɢɪɭɟɦɵɟ
ɢ
ɠɟɫɬɤɢɟ
ɨɛɨɥɨɱɤɢ
Ɇɟɬɨɞ
ɧɟɣɪɨɧɧɵɯ
ɫɟɬɟɣ
ɄɚɤɄɚɤ
ɨɩɪɟɞɟɥɢɬɶɨɩɪɟɞɟɥɢɬɶ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɞɥɹɞɥɹ
CGCG--ɦɨɞɟɥɢɦɨɞɟɥɢ ??
•• ǜǻDZǰǻǺǷǭǜǻDZǰǻǺǷǭ
ǽDzǴȀǸȉǿǭǿǻǯǽDzǴȀǸȉǿǭǿǻǯ
ǼǻDZǼǻDZ
ȊǷǾǼDzǽǵǹDzǺǿȊǷǾǼDzǽǵǹDzǺǿ..•• ǜǻDZǰǻǺǷǭǜǻDZǰǻǺǷǭ
ǽDzǴȀǸȉǿǭǿǻǯǽDzǴȀǸȉǿǭǿǻǯ
ǼǻDZǼǻDZ
ǭǿǻǹǵǾǿǵȄDzǾǷǻDzǭǿǻǹǵǾǿǵȄDzǾǷǻDz ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz..
ǕǿDzǽǭǿǵǯǺǭȌǕǿDzǽǭǿǵǯǺǭȌǎǻǸȉȃǹǭǺǻǯǾǷǭȌǎǻǸȉȃǹǭǺǻǯǾǷǭȌ
ǵǺǯDzǽǾǵȌǵǺǯDzǽǾǵȌ1
meso-scale
atomistic
g(R) + kT
g(R)
eff eff
i iu u lni
+
⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠
0effu = ɉɨɬɟɧɰɢɚɥ
ɫɪɟɞɧɟɣ
ɫɢɥɵ: -kT ln
g(R)atomistic
ueff
ȻɢɨɧɚɧɨɦɨɬɨɪȻɢɨɧɚɧɨɦɨɬɨɪ
(Flagellum)(Flagellum)
ǼȓȈȋȍȓȓțȔ
-
ȔȖȓȍȒțȓȧȘȕȣȑ
ȔȖȚȖȘ
(ȕȈȕȖȔȈȠȐȕȈ) ȐșȗȖȓȤȏțȍȔȣȑ
ȉȈȒȚȍȘȐȧȔȐ
Ȍȓȧ
ȗȘȖȌȊȐȎȍȕȐȧ
ȟȍȘȍȏ
șȘȍȌț. ǩȈȒȚȍȘȐȈȓȤȕȣȑ
flagellum ȥȚȖ
șȗȐȘȈȓȤȕȖȍ
ȊȖȓȖȒȕȖ
ȒȖȚȖȘȖȍ
ȊȘȈȡȈȍȚșȧ
ȒȈȒ
"ȕȈȊȍșȕȖȑ
ȔȖȚȖȘ".
ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ
ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ
ɦɨɞɟɥɢɦɨɞɟɥɢ
((ShapeShape--Based Coarse Graining)Based Coarse Graining)
ɈɛɨɥɨɱɤɢɈɛɨɥɨɱɤɢ
ɜɢɪɭɫɨɜɜɢɪɭɫɨɜ
((ɤɚɩɫɢɞɵɤɚɩɫɢɞɵ))
ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ
ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢǛǰǽȀǮǸDzǺǺȈDzǛǰǽȀǮǸDzǺǺȈDz
ǹǻDZDzǸǵǹǻDZDzǸǵ
((Patchy Particles Patchy Particles ––
""ǜȌǿǺǵǾǿȈDzǜȌǿǺǵǾǿȈDz
ȄǭǾǿǵȃȈȄǭǾǿǵȃȈ""))
12 X
Patchy ParticlePatchy Particle
ɉɪɨɰɟɫɫɵɉɪɨɰɟɫɫɵ
ɫɚɦɨɫɛɨɪɤɢɫɚɦɨɫɛɨɪɤɢɈɝɪɭɛɥɟɧɧɵɟɈɝɪɭɛɥɟɧɧɵɟ
ɦɨɞɟɥɢɦɨɞɟɥɢ
((Patchy ParticlesPatchy Particles))
•
Ɇɚɬɟɪɢɚɥɵ, ɫɨɫɬɨɹɳɢɟ
ɢɡ
ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɯ
ɝɪɚɧɭɥ•
ɉɟɫɨɤ, ɫɧɟɝ,
ɝɪɚɜɢɣ, ɤɪɭɩɚ
ɢ
ɨɪɟɲɤɢ•
ɉɨɜɟɞɟɧɢɟ
ɭɩɪɚɜɥɹɟɬɫɹ
ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦɢ
ɫɢɥɚɦɢ•
Ɍɪɟɧɢɟ, ɝɪɚɜɢɬɚɰɢɹ, ɮɨɪɦɚ
ɱɚɫɬɢɰ
ȽɪɚɧɭɥɹɪɧɵɟȽɪɚɧɭɥɹɪɧɵɟ
ɦɨɞɟɥɢɦɨɞɟɥɢ
ɊɟɲɟɬɨɱɧɵɟɊɟɲɟɬɨɱɧɵɟ
((ɞɢɫɤɪɟɬɧɵɟɞɢɫɤɪɟɬɧɵɟ) ) ɦɨɞɟɥɢɦɨɞɟɥɢ
CC BB AA
DD EEİED
İEA
İEC
İEB
1.
ɉɨɥɨɠɟɧɢɟ
ɱɚɫɬɢɰ
ɜ
ɩɪɨɫɬɪɚɧɫɬɜɟ
ɨɝɪɚɧɢɱɟɧɨ
ɭɡɥɚɦɢ
ɩɪɚɜɢɥɶɧɨɣ
ɪɟɲɟɬɤɢ.2.
ȼɡɚɢɦɨɞɟɣɫɬɜɭɸɬ
ɬɨɥɶɤɨ
ɱɚɫɬɢɰɵ
ɜ
ɫɨɫɟɞɧɢɯ
ɭɡɥɚɯ.3.
ɉɟɪɟɫɟɱɟɧɢɹ
ɰɟɩɢ
ɡɚɩɪɟɳɟɧɵ.
AA AA BB BB AB ABE N N Nε ε ε= + +
ɐɟɩɶ
ɫ
"ɮɥɭɤɬɭɢɪɭɸɳɢɦɢ" ɫɜɹɡɹɦɢ(bond fluctuation model)
"Ɋɟɩɬɚɰɢɨɧɧɚɹ" ɦɨɞɟɥɶ
ǙǺǻǰǻǰǽǭǺǺǵǷǏǻǽǻǺǻǰǻ
ȾɢɫɫɢɩɚɬɢɜɧɚɹȾɢɫɫɢɩɚɬɢɜɧɚɹ ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ ɱɚɫɬɢɰɱɚɫɬɢɰ (DPD)(DPD)
DPD-ȄǭǾǿǵȃǭ
ǞǯǻǶǾǿǯǭ
DPD ȄǭǾǿǵȃȈ
∑ −−=ψl
lkk ss )(/)()( rxrxx
)/exp()( 22 dxs −=x
∑ψ=i
ikk mM )(x
i
i
ikk mvxP ∑ψ= )(
∑ ∑ ⎟⎟⎠
⎞⎜⎜⎝
⎛+ψ=+
<i ij
ijMDiikkkk rUmvUVM )()( 2
2
12
2
1 x
kkkk M/PVr ≡=&
ȾɢɫɫɢɩɚɬɢɜɧɚɹȾɢɫɫɢɩɚɬɢɜɧɚɹ ɞɢɧɚɦɢɤɚɞɢɧɚɦɢɤɚ ɱɚɫɬɢɰɱɚɫɬɢɰ (DPD)(DPD)
V2
V1
F1dissipative
F2dissipative
F1random
F2random
RandomDissCons
ij ijijijFFFF ++=
"Ȼɥɨɛ"(ɫɬɚɬ. ɫɟɝɦɟɧɬ)
ijijij
C
ij ra rF )(ω=
ijijijij
D
ij r rvrF ))((2 ⋅γω−=
ijijijB
R
ij rTk rF )(2 ωξγ=
⎩⎨⎧
>≤−
=ωcutij
cutijcutij
ij rr
rrrrr
0
/1)(
);;( κδχ= solvFHij fa
)'(2)'()( ttTktt ijB
R
j
R
i −δδγδ= αββα FF
ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ
ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ
ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɍɪɨɤɍɪɨɤ
ʋʋ 11
Ɇɢɤɪɨɮɚɡɧɨɟ
ɪɚɡɞɟɥɟɧɢɟ:Ɇɚɫɲɬɚɛ
ɧɚɧɨɫɬɪɭɤɬɭɪ
~10-100 ɧɦ
100 ɧɦ
ɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹɋɚɦɨɨɪɝɚɧɢɡɚɰɢɹ
ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ
ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɍɪɨɤɍɪɨɤ
ʋʋ 22
ɑɚɫɬɢɰɵ ɉɨɥɟɜɨɟ
ɩɪɟɞɫɬɚɜɥɟɧɢɟ
LAM HEX BCC GYR
ȾɢɡɚɣɧȾɢɡɚɣɧ
ɩɨɥɢɦɟɪɧɵɯɩɨɥɢɦɟɪɧɵɯ
ɧɚɧɨɫɬɪɭɤɬɭɪɧɚɧɨɫɬɪɭɤɬɭɪ: : ɄɪɚɫɨɬɚɄɪɚɫɨɬɚ
ɇɚɧɨɦɢɪɚɇɚɧɨɦɢɪɚ
ɎɢɡɢɱɟɫɤɢɣɎɢɡɢɱɟɫɤɢɣ
ɫɢɧɬɟɡɫɢɧɬɟɡ: : ɂɧɠɟɧɟɪɢɹɂɧɠɟɧɟɪɢɹ
ɧɚɧɨɫɬɪɭɤɬɪɧɚɧɨɫɬɪɭɤɬɪ
timeɝɶɭɫɛɝɦɣɝɛɨɣɠ
~5 nm 30-50% ɪɩɫ
ɇɚɧɨɩɨɪɢɫɬɵɟ
ɦɚɬɟɪɢɚɥɵ
(ɦɟɦɛɪɚɧɵ, ɧɚɧɨɮɢɥɶɬɪɵ…)
ǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDzǙȀǸȉǿǵǹǭǾȅǿǭǮǺǻDz
ǹǻDZDzǸǵǽǻǯǭǺǵDzǹǻDZDzǸǵǽǻǯǭǺǵDz:: ǤǭǾǿǵȃȈǤǭǾǿǵȃȈ
+ + ǜǻǸȌǜǻǸȌ
Ƚɥɚɜɧɚɹ
ɢɞɟɹ:
Ⱦɟɤɨɦɩɨɡɢɰɢɹ
ɫɥɨɠɧɨɣ
ɫɢɫɬɟɦɵ
ɧɚ
2 ɱɚɫɬɢ:
Subsystem A(ɨɫɧɨɜɧɨɣ
ɢɧɬɟɪɟɫ)
Subsystem B(ɤɨɧɬɢɧɭɚɥɶɧɵɣ
ɮɨɧ)
Ɇɟɬɨɞɵ
ɱɚɫɬɢɰ(MC, MD, DPD)
ɉɨɥɟɜɨɟ
ɨɩɢɫɚɧɢɟ(RISM/PRISM, SCFT, DDFT)
ɑɚɫɬɢɰɵɑɚɫɬɢɰɵ ɉɨɥɟɉɨɥɟ
ǑǵǺǭǹǵȄDzǾǷǭȌǑǵǺǭǹǵȄDzǾǷǭȌ
ǿDzǻǽǵȌǿDzǻǽǵȌ
ȁȀǺǷȃǵǻǺǭǸǭȁȀǺǷȃǵǻǺǭǸǭ
ǼǸǻǿǺǻǾǿǵǼǸǻǿǺǻǾǿǵ
ȼ
ɨɬɥɢɱɢɟ
ɨɬ
ɦɟɬɨɞɨɜ
ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɨɝɨ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ
(ɬɚɤɢɯ, ɤɚɤ
Ɇɨɧɬɟ-Ʉɚɪɥɨɢɥɢ
ɦɨɥɟɤɭɥɹɪɧɚɹ
ɞɢɧɚɦɢɤɚ), ɝɞɟ
ɜɵɱɢɫɥɟɧɢɹ
ɩɪɨɜɨɞɹɬɫɹ
ɞɥɹ
ɚɬɨɦɨɜ
ɢɥɢ
ɦɨɥɟɤɭɥ, ɜɦɟɡɨɫɤɨɩɢɱɟɫɤɨɦ
ɦɨɞɟɥɢɪɨɜɚɧɢɢ
ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ
ɩɨɜɟɞɟɧɢɟɤɨɥɥɟɤɬɢɜɧɵɯ
ɩɟɪɟɦɟɧɧɵɯ
–
ɮɭɧɤɰɢɣ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɩɥɨɬɧɨɫɬɟɣ
ɢ
ɩɨɥɟɣ.
),()(
)]([F),( 2 tt
tr
r
rrα
α
αα
α η+δφφδ
∇Λ=∂
φ∂
F
–
ɮɭɧɤɰɢɨɧɚɥ
ɫɜɨɛɨɞɧɨɣ
ɷɧɟɪɝɢɢ, Λα
–
ɤɨɷɮɮɢɰɢɟɧɬɵ
ɩɨɞɜɢɠɧɨɫɬɢ
ɤɨɦɩɨɧɟɧɬɚ
α, η
–ɫɬɨɯɚɫɬɢɱɟɫɤɢɣ
ɲɭɦ, ɪɚɫɩɪɟɞɟɥɟɧɢɟ
ɤɨɬɨɪɨɝɨ
ɩɨɞɱɢɧɹɟɬɫɹ
ɮɥɭɤɬɭɚɰɢɨɧɧɨ-ɞɢɫɫɢɩɚɬɢɜɧɨɣ
ɬɟɨɪɟɦɟ.
ɗɜɨɥɸɰɢɹ
ɥɨɤɚɥɶɧɨɣ
ɩɥɨɬɧɨɫɬɢ
φ(r) ɤɨɦɩɨɧɟɧɬɚ
Į:
)]([)()]/([F rrr φμ≡δφφδ ααα
ȼɜɨɞɹɬɫɹ
ɝɢɩɨɬɟɬɢɱɟɫɤɢɟ
ɜɧɟɲɧɢɟ
ɩɨɥɹ
ȦĮ
(r), ɤɨɬɨɪɵɟ
ɞɟɣɫɬɜɭɸɬ
ɧɚ
ɤɨɦɩɨɧɟɧɬɭ
α
ɢ
ɩɨɞɛɢɪɚɸɬɫɹ
ɬɚɤ, ɱɬɨ
ɜ
ɤɚɠɞɵɣ
ɦɨɦɟɧɬ
ɜɪɟɦɟɧɢ
t
ɪɚɫɩɪɟɞɟɥɟɧɢɟ
ɩɥɨɬɧɨɫɬɟɣ
φα
(r,t) ɨɬɜɟɱɚɟɬ
ɪɚɜɧɨɜɟɫɧɨɦɭ
ɫɨɫɬɨɹɧɢɸ
→ ɩɪɨɛɥɟɦɚ
ɜɵɱɢɫɥɟɧɢɹ
ɯɢɦɢɱɟɫɤɢɯ
ɩɨɬɟɧɰɢɚɥɨɜ
μα
(r) ɩɟɪɟɮɨɪɦɭɥɢɪɭɟɬɫɹ
ɜ
ɩɪɨɛɥɟɦɭ, ɫɜɹɡɚɧɧɭɸ
ɫ
ɜɵɱɢɫɥɟɧɢɟɦ
ɜɧɟɲɧɢɯ
(ɫɚɦɨɫɨɝɥɚɫɨɜɚɧɧɵɯ) ɩɨɥɟɣ
ȦĮ
(r).
Ɋɚɜɧɨɜɟɫɢɟ:
įF[φ]/įφĮ
= 0
ǗǭǷǗǭǷ
ȊǿǻȊǿǻ
ǽǭǮǻǿǭDzǿǽǭǮǻǿǭDzǿ
? ? ǜǽǻǾǿǻǶǜǽǻǾǿǻǶ
ǼǽǵǹDzǽǼǽǵǹDzǽ..
ɊɚɡɞɟɥɟɧɢɟɊɚɡɞɟɥɟɧɢɟ
ɫɦɟɫɢɫɦɟɫɢ
ɛɟɧɡɨɥɚɛɟɧɡɨɥɚ
ɫɫ
ɜɨɞɨɣɜɨɞɨɣ
(1:1(1:1
ɫɦɟɫɶɫɦɟɫɶ))ɉɨɥɟɜɨɣɉɨɥɟɜɨɣ
ɲɚɛɥɨɧɲɚɛɥɨɧ: Im3m : Im3m ((ɊɊ--ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ
ɒɜɚɪɰɚɒɜɚɪɰɚ))
MDMD
ɎɢɧɚɥɶɧɚɹɎɢɧɚɥɶɧɚɹ
ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ
MD/SCFTMD/SCFTSCFTSCFT
ɆɟɯɚɧɢɤɚɆɟɯɚɧɢɤɚ
ɫɩɥɨɲɧɨɣɫɩɥɨɲɧɨɣ
ɫɪɟɞɵɫɪɟɞɵ::ɆɟɬɨɞɆɟɬɨɞ
ɤɨɧɟɱɧɵɯɤɨɧɟɱɧɵɯ
ɷɥɟɦɟɧɬɨɜɷɥɟɦɟɧɬɨɜ
x1 x2 x3 x4 x5 x6
U1
U6
U5U4
U3U2
U
1 2 3 4 5
a b
1
2
3
N(r)
N(r)+dN(r)
dx
q(r)(x)
i
j
u(r)(x) – ɩɟɪɟɦɟɳɟɧɢɟ
ɭɡɥɚq(r)(x) – ɢɧɬɟɧɫɢɜɧɨɫɬɶ
ɧɚɝɪɭɡɤɢq(r)(x)dx – ɧɚɝɪɭɡɤɚN(r)(x) – ɜɧɭɬɪɟɧɧɹɹ
ɫɢɥɚdN(r) + q(r)(x)dx = 0 – ɪɚɜɧɨɜɟɫɢɟ
ui
uj
)(
2
)(2)(
)()()(
rr
r
rrr
qdx
udc
dx
ducN
=−
=
ǔǭǷǻǺ
ǐȀǷǭ:
DZǭǯǸDzǺǵDz
ǞDZǯǵǰǻǯǻDz
ǺǭǼǽȌdzDzǺǵDz
ǝǭǾǼǽDzDZDzǸDzǺǵDz
ǺǭǼǽȌdzDzǺǵǶǼǽǵ
DZDzȁǻǽǹǭȃǵǵ
ǹDzǹǮǽǭǺȈ
ɆɟɬɨɞɆɟɬɨɞ
ɤɨɧɟɱɧɵɯɤɨɧɟɱɧɵɯ
ɷɥɟɦɟɧɬɨɜɷɥɟɦɟɧɬɨɜɆɟɦɛɪɚɧɚ
ɬɨɩɥɢɜɧɵɯ
ɷɥɟɦɟɧɬɨɜ
ɉɟɪɢɞɢɧɚɦɢɤɚɉɟɪɢɞɢɧɚɦɢɤɚ
((PeridynamicsPeridynamics
= = PeriPeri
+ + DynaDyna))
∫ +−′−′=ρ ′R
x txbdVxxxtxutxuftxux ),(];);,(),([),()( &&
ɍɪɚɜɧɟɧɢɟ
ɞɜɢɠɟɧɢɹ:
x
x'
f
–
ɩɥɨɬɧɨɫɬɶ
ɫɢɥ
(x'→x)ρ(x) –
ɩɥɨɬɧɨɫɬɶ
ɦɚɬɟɪɢɚɥɚu
–
ɜɟɤɬɨɪ
ɫɦɟɳɟɧɢɹ
V
ɉɟɪɢɞɢɧɚɦɢɤɚ
–
ɝɢɛɪɢɞ
ɦɨɥɟɤɭɥɹɪɧɨɣ
ɞɢɧɚɦɢɤɢ
ɢ
ɤɥɚɫɫɢɱɟɫɤɨɣ
ɬɟɨɪɢɢ
ɷɥɚɫɬɢɱɧɨɫɬɢ
f
= fbond
+ f
short
Ʌɸɛɨɣ
ɦɚɬɟɪɢɚɥɶɧɵɣ
ɩɪɟɞɦɟɬ
−
ɷɬɨ
ɜɫɟɝɨ
ɥɢɲɶ ɫɤɨɩɥɟɧɢɟ
ɚɬɨɦɨɜ
ɜ
ɩɪɨɫɬɪɚɧɫɬɜɟ. Ɍɨ, ɤɚɤ
ɷɬɢ
ɚɬɨɦɵ ɫɨɛɪɚɧɵ
ɜ
ɫɬɪɭɤɬɭɪɭ, ɨɩɪɟɞɟɥɹɟɬ, ɱɬɨ
ɷɬɨ
ɛɭɞɟɬ
ɡɚ ɩɪɟɞɦɟɬ. ɂ
ɦɵ
ɬɨɥɶɤɨ
ɞɢɪɢɠɢɪɭɟɦ
ɨɪɤɟɫɬɪɨɦ
ɢɡ
ɷɬɢɯ ɚɬɨɦɧɵɯ
ɫɬɪɭɤɬɭɪ. ɗɬɨɬ
ɨɪɤɟɫɬɪ
ɫɭɳɟɫɬɜɨɜɚɥ
ɫ ɫɨɬɜɨɪɟɧɢɹ
ɦɢɪɚ
ɢ
ɥɢɲɶ
ɠɞɟɬ, ɤɨɝɞɚ
ɩɨɹɜɢɬɫɹ
ɞɢɪɢɠɟɪ
...
ɋɬɚɧɢɫɥɚɜ
Ʌɟɦ, 1982 ɝ.
+ +
+
+
+
+
+
_
__
_
_
_
_
ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵ: : ɈɩɪɟɞɟɥɟɧɢɟɈɩɪɟɞɟɥɟɧɢɟ
ɉɨɥɢɷɥɟɤɬɪɨɥɢɬ
==ɩɨɥɢɦɟɪɩɨɥɢɦɟɪ
ɫɫ
ɡɚɪɹɠɟɧɧɵɦɢɡɚɪɹɠɟɧɧɵɦɢ
ɦɨɧɨɦɟɪɚɦɢɦɨɧɨɦɟɪɚɦɢ
ȾɢɫɫɨɰɢɚɰɢɹȾɢɫɫɨɰɢɚɰɢɹ::ɇɟɣɬɪɚɥɶɧɵɣɇɟɣɬɪɚɥɶɧɵɣ
ɦɨɧɨɦɟɪɦɨɧɨɦɟɪ
⇔⇔ɡɚɪɹɠɟɧɧɵɣɡɚɪɹɠɟɧɧɵɣ
ɦɨɧɨɦɟɪɦɨɧɨɦɟɪ
+ + ɤɨɧɬɪɢɨɧɤɨɧɬɪɢɨɧ
ɑɢɫɥɨɑɢɫɥɨ
ɤɨɧɬɪɢɨɧɨɜɤɨɧɬɪɢɨɧɨɜ
= = ɱɢɫɥɨɱɢɫɥɨ
ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ
ɦɨɧɨɦɟɪɨɜɦɨɧɨɦɟɪɨɜ(N(N++
= N= N--))
ɉɨɥɢɦɟɪ
ɉɨɞɜɢɠɧɵɣ
ɤɨɧɬɪɢɨɧ
ɉɨɥɢɚɧɢɨɧɵɉɨɥɢɚɧɢɨɧɵ
ɢɢ
ɩɨɥɢɤɚɬɢɨɧɵɩɨɥɢɤɚɬɢɨɧɵɉɪɢɦɟɪɵɉɪɢɦɟɪɵ::
(a) sodium (a) sodium polyacrylatepolyacrylate
(b) sodium (b) sodium polymetacrylatepolymetacrylate
(c) (c) polydiallyldimethylammoniumpolydiallyldimethylammonium
chloridechloride
(d) (d) ȾɇɄȾɇɄ
((ɡɚɪɹɞɡɚɪɹɞ
--ee
ɧɚɧɚ
1.7 1.7 ɧɦɧɦ))
(e) (e) ȽɢɫɬɨɧȽɢɫɬɨɧ
––
ɧɭɤɥɟɨɩɪɨɬɟɢɧɧɭɤɥɟɨɩɪɨɬɟɢɧ
(+170(+170e)e)CH
2
CHCH
CH2
N+
CH2
CH2CH
3CH
3
CH3CH
3
CH2
CHCH3
CH3
CO
ONa
+
Cl
CH2
CCH3
CH3
CO
O
CH3
Na+
(a) (b)
(c)
(d) (e)
ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵɉɨɥɢɷɥɟɤɬɪɨɥɢɬɵ
ɋɢɥɶɧɨɋɢɥɶɧɨ
ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟȻɨɥɶɲɚɹȻɨɥɶɲɚɹ
ɞɨɥɹɞɨɥɹ
ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ
ɡɜɟɧɶɟɜɡɜɟɧɶɟɜ((ϕϕ
= = NNqq
/ N / N ≈≈
1)1)
ɋɢɥɶɧɨɋɢɥɶɧɨ
ɩɨɥɹɪɧɚɹɩɨɥɹɪɧɚɹ
ɫɪɟɞɚɫɪɟɞɚ
((ɜɨɞɚɜɨɞɚ, , εε
≈≈
8080))
ɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ
ɞɨɦɢɧɢɪɭɟɬɞɨɦɢɧɢɪɭɟɬ
ɋɥɚɛɨɋɥɚɛɨ
ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟɆɚɥɚɹɆɚɥɚɹ
ɞɨɥɹɞɨɥɹ
ɡɚɪɹɠɟɧɧɵɯɡɚɪɹɠɟɧɧɵɯ
ɡɜɟɧɶɟɜɡɜɟɧɶɟɜ((ϕϕ
= = NNqq
/ N / N <<<<
1)1)
ɋɥɚɛɨɋɥɚɛɨ
ɩɨɥɹɪɧɚɹɩɨɥɹɪɧɚɹ
ɫɪɟɞɚɫɪɟɞɚ
((εε
< 10< 10))
ɄɭɥɨɧɨɜɫɤɢɟɄɭɥɨɧɨɜɫɤɢɟ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹɤɨɧɤɭɪɢɪɭɸɬɤɨɧɤɭɪɢɪɭɸɬ
ɫɫ
ɞɢɫɩɟɪɫɢɨɧɧɵɦɢɞɢɫɩɟɪɫɢɨɧɧɵɦɢ
ɉɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣɉɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣ
ɢɢ
ɢɨɧɨɦɟɪɧɵɣɢɨɧɨɦɟɪɧɵɣ
ɪɟɠɢɦɵɪɟɠɢɦɵ
ɉɨɥɹɪɧɵɣɉɨɥɹɪɧɵɣ
ɪɚɫɬɜɨɪɢɬɟɥɶɪɚɫɬɜɨɪɢɬɟɥɶ::
εε
>> 1, >> 1, ΓΓ
< 1< 1
→→
ɩɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣɩɨɥɢɷɥɟɤɬɪɨɥɢɬɧɵɣ
ɪɟɠɢɦɪɟɠɢɦɈɪɝɚɧɢɱɟɫɤɢɣɈɪɝɚɧɢɱɟɫɤɢɣ
ɪɚɫɬɜɨɪɢɬɟɥɶɪɚɫɬɜɨɪɢɬɟɥɶ::
εε
~ 1, ~ 1, ΓΓ
>> 1>> 1
→→
ɢɨɧɨɦɟɪɧɵɣɢɨɧɨɦɟɪɧɵɣ
ɪɟɠɢɦɪɟɠɢɦ
u (r) = q q / rc 1 2 ε
q1 q2
rɗɥɟɤɬɪɨɫɬɚɬɢɤɚɗɥɟɤɬɪɨɫɬɚɬɢɤɚ::
ɉɨɬɟɧɰɢɚɥɶɧɚɹ
ɷɧɟɪɝɢɹ:
e2/εr0
Ɍɟɩɥɨɜɚɹ
ɷɧɟɪɝɢɹ:
~kT
ɉɚɪɚɦɟɬɪ
ɫɜɹɡɢ:
Γ
= e2/εr0 kT
Ⱦɥɢɧɚ
Ȼɶɟɪɪɭɦɚ:
lB
= e2/εkT
|q|q11
| = || = |--qq22
| = | = ɷɥɟɦɟɧɬɚɪɧɵɣɷɥɟɦɟɧɬɚɪɧɵɣ
ɡɚɪɹɞɡɚɪɹɞ ((ee))
ȼɨɞɚȼɨɞɚ
ɩɪɢɩɪɢ
T = 298 KT = 298 K::σσ
≈≈
3.5 3.5 ÅÅ; ; εε
= 81= 81llBB
= 7.1 = 7.1 ÅÅΓΓ
≈≈
22
ȻɟɧɡɨɥȻɟɧɡɨɥ: : ΓΓ
> 20> 20
_
+__
ɂɨɧɨɦɟɪɵɂɨɧɨɦɟɪɵȼȼ
ɨɪɝɚɧɢɱɟɫɤɨɦɨɪɝɚɧɢɱɟɫɤɨɦ
ɪɚɫɬɜɨɪɢɬɟɥɟɪɚɫɬɜɨɪɢɬɟɥɟ
ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ ɤɨɧɞɟɧɫɢɪɭɸɬɫɹɤɨɧɞɟɧɫɢɪɭɸɬɫɹ
ɧɚɧɚ
ɦɨɧɨɦɟɪɚɯɦɨɧɨɦɟɪɚɯ
→→ɮɨɪɦɢɪɭɸɬɫɹɮɨɪɦɢɪɭɸɬɫɹ
ɢɨɧɧɵɟɢɨɧɧɵɟ
ɩɚɪɵɩɚɪɵ
ɂɨɧɧɚɹɂɨɧɧɚɹ
ɩɚɪɚɩɚɪɚ
= = ɮɥɭɤɬɭɢɪɭɸɳɢɣɮɥɭɤɬɭɢɪɭɸɳɢɣ
ɞɢɩɨɥɶɞɢɩɨɥɶ ɋɢɥɶɧɨɟɋɢɥɶɧɨɟ
ɞɢɩɨɥɶɞɢɩɨɥɶ--ɞɢɩɨɥɶɧɨɟɞɢɩɨɥɶɧɨɟ
ɩɪɢɬɹɠɟɧɢɟɩɪɢɬɹɠɟɧɢɟ →→ɚɫɫɨɰɢɚɰɢɹɚɫɫɨɰɢɚɰɢɹ
ɞɢɩɨɥɟɣɞɢɩɨɥɟɣ
→→ɮɨɪɦɢɪɨɜɚɧɢɟɮɨɪɦɢɪɨɜɚɧɢɟ
ɦɭɥɶɬɢɩɥɟɬɨɜɦɭɥɶɬɢɩɥɟɬɨɜ::
ɆɭɥɶɬɢɩɥɟɬɆɭɥɶɬɢɩɥɟɬ
= = ɚɝɪɟɝɚɬɚɝɪɟɝɚɬ
ɢɡɢɡ
ɞɢɩɨɥɟɣɞɢɩɨɥɟɣ
ȾɚɥɶɧɨɞɟɣɫɬɜɢɟȾɚɥɶɧɨɞɟɣɫɬɜɢɟ
←←
LL →→2D box2D box 3D box3D box
∑∑≠
ε +=
m mr
N
ji ij
ji
CL
qqU 1
mmxx , m, myy , , mmzz = = 0,1,2,0,1,2,……,,∞∞
1.5
1.0
0.5
0.0
-0.5
-1.0
4321
Lennard-JonesCoulomb + LJ
distance (r)
Ene
rgy,
u(r
)
ɆɚɤɪɨɢɨɧɆɚɤɪɨɢɨɧ
+ + ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ
Sun
# run# run0
20
40
60
80
100
1 2
ΓΓ
Simulation protocolSimulation protocol
+1e
-20e
ɋɢɥɶɧɵɟɋɢɥɶɧɵɟ
ɥɚɬɟɪɚɥɶɧɵɟɥɚɬɟɪɚɥɶɧɵɟ ɤɨɪɪɟɥɹɰɢɢɤɨɪɪɟɥɹɰɢɢ. . ɄɨɧɬɪɢɨɧɵɄɨɧɬɪɢɨɧɵ ɮɨɪɦɢɪɭɸɬɮɨɪɦɢɪɭɸɬ
ɫɬɪɭɤɬɭɪɭɫɬɪɭɤɬɭɪɭ
ɬɢɩɚɬɢɩɚ
1D 1D ɤɪɢɫɬɚɥɥɚɤɪɢɫɬɚɥɥɚ
ȼɢɝɧɟɪɚȼɢɝɧɟɪɚ..
ȽɢɝɚɧɬɫɤɚɹȽɢɝɚɧɬɫɤɚɹ
ɡɧɚɤɨɜɚɹɡɧɚɤɨɜɚɹ
ɢɧɜɟɪɫɢɹɢɧɜɟɪɫɢɹ
Sun
-24e9e -1e
ΓΓ
# run# run0
10
20
30
40
50
1 2
Simulation protocolSimulation protocol ɆɚɤɪɨɢɨɧɆɚɤɪɨɢɨɧ
+ + ɦɭɥɶɬɢɜɚɥɟɧɬɧɵɟɦɭɥɶɬɢɜɚɥɟɧɬɧɵɟ
ɤɨɧɬɪɢɨɧɵɤɨɧɬɪɢɨɧɵ
+ + ɦɨɧɨɜɚɥɟɧɬɧɵɟɦɨɧɨɜɚɥɟɧɬɧɵɟ
ɢɨɧɵɢɨɧɵ
ɉɨɫɥɟɉɨɫɥɟ
ɤɨɧɞɟɧɫɚɰɢɢɤɨɧɞɟɧɫɚɰɢɢ
ɦɚɤɪɨɢɨɧɦɚɤɪɨɢɨɧ
ɩɟɪɟɡɚɪɹɠɚɟɬɫɹɩɟɪɟɡɚɪɹɠɚɟɬɫɹ: : ɟɝɨɟɝɨ
ɡɚɪɹɞɡɚɪɹɞ
ɜɛɥɢɡɢɜɛɥɢɡɢ
ɩɨɜɟɪɯɧɨɫɬɢɩɨɜɟɪɯɧɨɫɬɢ
ɦɟɧɹɟɬɦɟɧɹɟɬ
ɡɧɚɤɡɧɚɤ((ɨɬɨɬ
––2424ee ɞɨɞɨ
66××99e e ––
2424e e = +30= +30ee))
[A. [A. GrosbergGrosberg
and B. and B. ShklovskiiShklovskii]]
ɂɨɧɧɵɟɂɨɧɧɵɟ
ɮɪɚɤɬɚɥɵɮɪɚɤɬɚɥɵΓΓ
> 100 > 100 →→
ɤɪɢɫɬɚɥɥɤɪɢɫɬɚɥɥ
ȼɢɝɧɟɪɚȼɢɝɧɟɪɚ
= = ɮɪɚɤɬɚɥɶɧɵɣɮɪɚɤɬɚɥɶɧɵɣ
ɨɛɴɟɤɬɨɛɴɟɤɬ
ɐɟɩɶɐɟɩɶ
+ + ɦɚɤɪɨɢɨɧɦɚɤɪɨɢɨɧ
Sun
# run# run0
2
4
6
8
10
1 2 3 4 5
ΓΓ
ȾɥɹȾɥɹ
ɨɪɝɚɧɢɡɚɰɢɢɨɪɝɚɧɢɡɚɰɢɢ
ȾɇɄȾɇɄ
ɜɜ ɯɪɨɦɚɬɢɧɯɪɨɦɚɬɢɧ, , ɉɪɢɪɨɞɚɉɪɢɪɨɞɚ
ɢɫɩɨɥɶɡɭɟɬɢɫɩɨɥɶɡɭɟɬ
ɝɢɫɬɨɧɵɝɢɫɬɨɧɵ
–– ɩɪɨɬɟɢɧɵɩɪɨɬɟɢɧɵ
ɫɫ
ɨɝɪɨɦɧɵɦɨɝɪɨɦɧɵɦ ɩɨɥɨɠɢɬɟɥɶɧɵɦɩɨɥɨɠɢɬɟɥɶɧɵɦ
ɡɚɪɹɞɨɦɡɚɪɹɞɨɦ..
-1e
-1e
-1e-1e
-1e
+60e
ȾɇɄȾɇɄ: d = 2 : d = 2 ɧɦɧɦ, , ɡɚɪɹɞɡɚɪɹɞ
--ee
ɧɚɧɚ
1.7 1.7 ɧɦɧɦ
ɉɪɢɉɪɢ
ΓΓ
≥≥
10, 10, ɰɟɩɶɰɟɩɶ
ɮɨɪɦɢɪɭɟɬɮɨɪɦɢɪɭɟɬ ɜɢɬɤɢɜɢɬɤɢ
ɜɨɤɪɭɝɜɨɤɪɭɝ
ɦɚɤɪɨɢɨɧɚɦɚɤɪɨɢɨɧɚ. . ȼɢɬɤɢȼɢɬɤɢ ɭɤɥɚɞɵɜɚɸɬɫɹɭɤɥɚɞɵɜɚɸɬɫɹ
ɜɜ
ɫɨɥɟɧɨɢɞɫɨɥɟɧɨɢɞ..
ɐɟɩɶɐɟɩɶ
+ + ɦɚɤɪɨɢɨɧɵɦɚɤɪɨɢɨɧɵ: : ɋɚɦɨɫɛɨɪɤɚɋɚɦɨɫɛɨɪɤɚ
ɇɚɇɚ
ɛɨɥɶɲɢɯɛɨɥɶɲɢɯ
ɦɚɫɲɬɚɛɚɯɦɚɫɲɬɚɛɚɯ
ɨɞɧɨɢɦɟɧɧɨɨɞɧɨɢɦɟɧɧɨ
ɡɚɪɹɠɟɧɧɵɟɡɚɪɹɠɟɧɧɵɟ
ɫɮɟɪɵɫɮɟɪɵ ɨɬɬɚɥɤɢɜɚɸɬɫɹɨɬɬɚɥɤɢɜɚɸɬɫɹ
→→ ɨɠɟɪɟɥɶɟɨɠɟɪɟɥɶɟ
ɪɚɫɬɹɝɢɜɚɟɬɫɹɪɚɫɬɹɝɢɜɚɟɬɫɹ..
ɋɨɫɟɞɧɢɟɋɨɫɟɞɧɢɟ
ɜɢɬɤɢɜɢɬɤɢ
ɨɬɬɚɥɤɢɜɚɸɬɫɹɨɬɬɚɥɤɢɜɚɸɬɫɹ
ɢɢ ɮɨɪɦɢɪɭɸɬɮɨɪɦɢɪɭɸɬ
ɪɟɝɭɥɹɪɧɵɣɪɟɝɭɥɹɪɧɵɣ
ɫɨɥɟɧɨɢɞɫɨɥɟɧɨɢɞ..
ɑɬɨɑɬɨ
ɩɪɨɢɡɨɣɞɟɬɩɪɨɢɡɨɣɞɟɬ, , ɟɫɥɢɟɫɥɢ
ɞɥɢɧɚɞɥɢɧɚ
ɰɟɩɢɰɟɩɢ
ɜɟɥɢɤɚɜɟɥɢɤɚ? ? ɈɠɢɞɚɟɬɫɹɈɠɢɞɚɟɬɫɹ, , ɱɬɨɱɬɨ
ɱɚɫɬɶɱɚɫɬɶ
ɰɟɩɢɰɟɩɢ
ɛɭɞɟɬɛɭɞɟɬ ɮɨɪɦɢɪɨɜɚɬɶɮɨɪɦɢɪɨɜɚɬɶ
ɜɵɬɹɧɭɬɵɣɜɵɬɹɧɭɬɵɣ
ɯɜɨɫɬɯɜɨɫɬ..ȿɫɥɢȿɫɥɢ
ɰɟɩɶɰɟɩɶ
ɨɱɟɧɶɨɱɟɧɶ
ɞɥɢɧɧɚɹɞɥɢɧɧɚɹ
ɢɢ
ɩɪɢɫɭɬɫɬɜɭɟɬɩɪɢɫɭɬɫɬɜɭɟɬ ɦɧɨɝɨɦɧɨɝɨ
ɦɚɤɪɨɢɨɧɨɜɦɚɤɪɨɢɨɧɨɜ
→→ ɮɨɪɦɢɪɭɟɬɫɹɮɨɪɦɢɪɭɟɬɫɹ ɫɬɪɭɤɬɭɪɚɫɬɪɭɤɬɭɪɚ
ɬɢɩɚɬɢɩɚ
ɨɠɟɪɟɥɶɹɨɠɟɪɟɥɶɹ
((""beadsbeads--onon--stringstring"")): :
ɈɪɝɚɧɢɡɚɰɢɹɈɪɝɚɧɢɡɚɰɢɹ
ȾɇɄȾɇɄ
ɋɬɪɭɤɬɭɪɚɋɬɪɭɤɬɭɪɚ
ɬɢɩɚɬɢɩɚ
ɨɠɟɪɟɥɶɹɨɠɟɪɟɥɶɹ::ɄɚɠɞɚɹɄɚɠɞɚɹ
ɧɭɤɥɟɨɫɨɦɚɧɭɤɥɟɨɫɨɦɚ
ɫɨɞɟɪɠɢɬɫɨɞɟɪɠɢɬ ɨɞɢɧɨɞɢɧ
ɨɤɬɚɦɟɪɨɤɬɚɦɟɪ
ɫɫ
ɡɚɪɹɞɨɦɡɚɪɹɞɨɦ
+170+170ee..ɇɚɇɚ
ɨɤɬɚɦɟɪɨɤɬɚɦɟɪ
ɧɚɦɨɬɚɧɚɧɚɦɨɬɚɧɚ
ɰɟɩɶɰɟɩɶ
ȾɇɄȾɇɄ..
ɌɨɪɨɢɞɚɥɶɧɚɹɌɨɪɨɢɞɚɥɶɧɚɹ
ɨɪɝɚɧɢɡɚɰɢɹɨɪɝɚɧɢɡɚɰɢɹ
ȾɇɄȾɇɄ
Sun
ȽȽ
= 5= 5
ɄɨɧɞɟɧɫɚɰɢɹɄɨɧɞɟɧɫɚɰɢɹ
ɤɨɧɬɪɢɨɧɨɜɤɨɧɬɪɢɨɧɨɜ ɩɪɨɞɭɰɢɪɭɟɬɩɪɨɞɭɰɢɪɭɟɬ
ɩɪɢɬɹɠɟɧɢɟɩɪɢɬɹɠɟɧɢɟ..
ɂɨɧɵɂɨɧɵ
ɢɝɪɚɸɬɢɝɪɚɸɬ
ɪɨɥɶɪɨɥɶ ""ɢɨɧɧɨɝɨɢɨɧɧɨɝɨ
ɤɥɟɹɤɥɟɹ""
Electron micrograph of toroidal DNA,Electron micrograph of toroidal DNA,J.J.--L. L. SikoravSikorav
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